Neuroblastoma remains a fatal disease for a large percentage of patients, especially those with high-risk features who become resistant to conventional therapy. This study is a limited institution pilot study designed to investigate the combination of buthionine sulfoximine (BSO) and melphalan (LPAM) in high-risk neuroblastoma patients with progressive disease (a phase I/II study). Specific Aim 1: To determine the toxicity of the combination of BSO and LPAM in pediatric patients with progressive neuroblastoma. Specific Aim 2: To determine the pharmacokinetics of the combination of BSO and LPAM in pediatric patients. Specific Aim 3: To determine the ability of BSO to deplete glutathione from tumor in marrow, normal marrow cells, and peripheral blood lymphocytes in pediatric patients. Secondary Aim: To determine the response rate of neuroblastoma to BSO and LPAM within the confines of a pilot study.